Xiaoli, Xiaoqiang and Xiaohong, grade nine students of a certain school, went to the supermarket to participate in the social practice activities, in which they took part in the sales of certain fruits It is known that the purchase price of the fruit is 8 yuan / kg. Here is their conversation after the event Xiao Li: if you sell it at 10 yuan / kg, you can sell 100 kg per day Xiaoqiang: if you sell it at 13 yuan / kg, you can make a profit of 400 yuan per day Xiao Hong: through investigation and verification, I found that there is a functional relationship between the daily sales volume of Y kg and the sales unit price of X Yuan Xiaoqiang: I find that the daily sales volume is between 70kg and 100kg (1) Find the functional relationship between Y (kg) and X (yuan) (x > 0); (2) Suppose the daily profit of the supermarket is w yuan. When the unit price of the fruit is w yuan, what is the maximum profit? What is the maximum profit? PS: Digital conditions are different

Xiaoli, Xiaoqiang and Xiaohong, grade nine students of a certain school, went to the supermarket to participate in the social practice activities, in which they took part in the sales of certain fruits It is known that the purchase price of the fruit is 8 yuan / kg. Here is their conversation after the event Xiao Li: if you sell it at 10 yuan / kg, you can sell 100 kg per day Xiaoqiang: if you sell it at 13 yuan / kg, you can make a profit of 400 yuan per day Xiao Hong: through investigation and verification, I found that there is a functional relationship between the daily sales volume of Y kg and the sales unit price of X Yuan Xiaoqiang: I find that the daily sales volume is between 70kg and 100kg (1) Find the functional relationship between Y (kg) and X (yuan) (x > 0); (2) Suppose the daily profit of the supermarket is w yuan. When the unit price of the fruit is w yuan, what is the maximum profit? What is the maximum profit? PS: Digital conditions are different

Let the relation of quantity price function be y = KX + B, then
100=10k+b
400 / (13-8) = 13K + B, i.e. 80 = 13K + B
3k=-20
k=-20/3
b=500/3
therefore
（1）
Y = - 20x / 3 + 500 / 3 (70 ≤ y ≤ 100, i.e. 10 ≤ x ≤ 14.5)
（2）
W=y*(x-8)=-20x²/3+220x-4000/3
The opening of the quadratic function is downward, and the axis of symmetry is x = 220 / (40 / 3) = 16.5
The domain of definition is 10 ≤ x ≤ 14.5, which is an increasing function on the left side of the axis of symmetry
That is, when x = 14.5 yuan, W is the largest, and the profit W is 455 yuan

Xiaoli, Xiaoqiang and Xiaohong, the eighth graders of a certain school, went to a supermarket to participate in social practice activities. In the activities, they participated in the sales of a certain kind of fruit. It is known that the price of the fruit is 8 yuan / kg. The following is their dialogue after the activities. Xiaoli: if the price is 10 yuan / kg, 300 kg can be sold every day. Xiaoqiang: if the price is 13 yuan / kg Xiao Hong: through investigation and verification, I found that there is a functional relationship between the daily sales volume y (kg) and the unit price x (yuan). (1) find the functional relationship between Y (kg) and X (yuan) (x > 0); (2) suppose that the daily profit of the supermarket is w yuan, then what is the unit price, What's the biggest profit you can get every day? What is the maximum profit? [profit = sales volume × (sales unit price - purchase price)]

(1) When the unit price is 13 yuan / kg, the sales volume is: 75013 − 8 = 150 kg. Let y and X be y = KX + B (K ≠ 0), substituting (10300) and (13150) respectively into: 300 = 10K + B150 = 13K + B  k = − 50B = 800  y and X be y = - 50x + 800 (...)